Optimizing single Slater determinant for electronic Hamiltonian with Lagrange multipliers and Newton-Raphson methods as an alternative to ground state calculations via Hartree-Fock self consistent field

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Considering the emblematic Hartree-Fock (HF) energy expression with single Slater determinant and the ortho-normal molecular orbits (MO) in it, expressed as a linear combination (LC) of atomic orbits (LCAO) basis set functions, the HF energy expression is in fact a 4th order polynomial of the LCAO coefficients, which is relatively easy to handle. The energy optimization via the Variation Principle can be made with a Lagrange multiplier method to keep the ortho-normal property and the Newton-Raphson (NR) method to find the function minimum. It is an alternative to the widely applied HF self consistent field (HF-SCF) method which is based on unitary transformations and eigensolver during the SCF, and seems to have more convenient convergence property. This method is demonstrated for closed shell (even number of electrons and all MO are occupied with both, α and β spin electrons) and restricted (all MOs have single individual spatial orbital), but the extension of the method to open shell and/or unrestricted cases is straightforward.

Original languageEnglish
Title of host publicationInternational Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2018
EditorsT.E. Simos, T.E. Simos, T.E. Simos, T.E. Simos, Ch. Tsitouras, T.E. Simos
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735418547
DOIs
Publication statusPublished - Jul 24 2019
EventInternational Conference on Numerical Analysis and Applied Mathematics 2018, ICNAAM 2018 - Rhodes, Greece
Duration: Sep 13 2018Sep 18 2018

Publication series

NameAIP Conference Proceedings
Volume2116
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

ConferenceInternational Conference on Numerical Analysis and Applied Mathematics 2018, ICNAAM 2018
CountryGreece
CityRhodes
Period9/13/189/18/18

Fingerprint

Newton-Raphson method
multipliers
Lagrange multipliers
determinants
orbits
electronics
self consistent fields
ground state
shell
energy
electron
electrons
field method
methodology
electron spin
polynomials
orbitals
optimization
calculation
method

Keywords

  • Alternative method for Hartree-Fock self consistent field
  • Lagrange multipliers method to optimize single Slater determinant

ASJC Scopus subject areas

  • Ecology, Evolution, Behavior and Systematics
  • Ecology
  • Plant Science
  • Physics and Astronomy(all)
  • Nature and Landscape Conservation

Cite this

Kristyán, S. (2019). Optimizing single Slater determinant for electronic Hamiltonian with Lagrange multipliers and Newton-Raphson methods as an alternative to ground state calculations via Hartree-Fock self consistent field. In T. E. Simos, T. E. Simos, T. E. Simos, T. E. Simos, C. Tsitouras, & T. E. Simos (Eds.), International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2018 [450030] (AIP Conference Proceedings; Vol. 2116). American Institute of Physics Inc.. https://doi.org/10.1063/1.5114497

Optimizing single Slater determinant for electronic Hamiltonian with Lagrange multipliers and Newton-Raphson methods as an alternative to ground state calculations via Hartree-Fock self consistent field. / Kristyán, S.

International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2018. ed. / T.E. Simos; T.E. Simos; T.E. Simos; T.E. Simos; Ch. Tsitouras; T.E. Simos. American Institute of Physics Inc., 2019. 450030 (AIP Conference Proceedings; Vol. 2116).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Kristyán, S 2019, Optimizing single Slater determinant for electronic Hamiltonian with Lagrange multipliers and Newton-Raphson methods as an alternative to ground state calculations via Hartree-Fock self consistent field. in TE Simos, TE Simos, TE Simos, TE Simos, C Tsitouras & TE Simos (eds), International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2018., 450030, AIP Conference Proceedings, vol. 2116, American Institute of Physics Inc., International Conference on Numerical Analysis and Applied Mathematics 2018, ICNAAM 2018, Rhodes, Greece, 9/13/18. https://doi.org/10.1063/1.5114497
Kristyán S. Optimizing single Slater determinant for electronic Hamiltonian with Lagrange multipliers and Newton-Raphson methods as an alternative to ground state calculations via Hartree-Fock self consistent field. In Simos TE, Simos TE, Simos TE, Simos TE, Tsitouras C, Simos TE, editors, International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2018. American Institute of Physics Inc. 2019. 450030. (AIP Conference Proceedings). https://doi.org/10.1063/1.5114497
Kristyán, S. / Optimizing single Slater determinant for electronic Hamiltonian with Lagrange multipliers and Newton-Raphson methods as an alternative to ground state calculations via Hartree-Fock self consistent field. International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2018. editor / T.E. Simos ; T.E. Simos ; T.E. Simos ; T.E. Simos ; Ch. Tsitouras ; T.E. Simos. American Institute of Physics Inc., 2019. (AIP Conference Proceedings).
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